prodchisqpow  R Documentation 
Density, distribution function, quantile function and random generation for the distribution of the product of noncentral chisquares taken to powers.
dprodchisqpow(x, df, ncp=0, pow=1, log = FALSE, order.max=5)
pprodchisqpow(q, df, ncp=0, pow=1, lower.tail = TRUE, log.p = FALSE, order.max=5)
qprodchisqpow(p, df, ncp=0, pow=1, lower.tail = TRUE, log.p = FALSE, order.max=5)
rprodchisqpow(n, df, ncp=0, pow=1)
x, q 
vector of quantiles. 
df 
the vector of degrees of freedom.
This is recycled against the 
ncp 
the vector of noncentrality parameters.
This is recycled against the 
pow 
the vector of the power parameters.
This is recycled against the 
log 
logical; if TRUE, densities 
order.max 
the order to use in the approximate density, distribution, and quantile computations, via the GramCharlier, Edeworth, or CornishFisher expansion. 
p 
vector of probabilities. 
n 
number of observations. 
log.p 
logical; if TRUE, probabilities p are given
as 
lower.tail 
logical; if TRUE (default), probabilities are

Let X_i \sim \chi^2\left(\delta_i, \nu_i\right)
be independently distributed noncentral chisquares, where \nu_i
are the degrees of freedom, and \delta_i
are the
noncentrality parameters.
Let p_i
be given constants. Suppose
Y = \prod_i X_i^{p_i}.
Then Y
follows a product of chisquares to power distribution.
dprodchisqpow
gives the density, pprodchisqpow
gives the
distribution function, qprodchisqpow
gives the quantile function,
and rprodchisqpow
generates random deviates.
Invalid arguments will result in return value NaN
with a warning.
The PDF, CDF, and quantile function are approximated, via the Edgeworth or Cornish Fisher approximations, which may not be terribly accurate in the tails of the distribution. You are warned.
The distribution parameters are not recycled
with respect to the x, p, q
or n
parameters,
for, respectively, the density, distribution, quantile
and generation functions. This is for simplicity of
implementation and performance. It is, however, in contrast
to the usual R idiom for dpqr functions.
The PDQ functions are computed by translation of the sum of log chisquares distribution functions.
Steven E. Pav shabbychef@gmail.com
Pav, Steven. Moments of the log noncentral chisquare distribution. https://arxiv.org/abs/1503.06266
The sum of log of chisquares distribution,
dsumlogchisq
,
psumlogchisq
,
qsumlogchisq
,
rsumlogchisq
,
The upsilon distribution,
dupsilon
,
pupsilon
,
qupsilon
,
rupsilon
.
The sum of chisquare powers distribution,
dsumchisqpow
,
psumchisqpow
,
qsumchisqpow
,
rsumchisqpow
.
df < c(100,20,10)
ncp < c(5,3,1)
pow < c(1,0.5,1)
rvs < rprodchisqpow(128, df, ncp, pow)
dvs < dprodchisqpow(rvs, df, ncp, pow)
qvs < pprodchisqpow(rvs, df, ncp, pow)
pvs < qprodchisqpow(ppoints(length(rvs)), df, ncp, pow)
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